Magnetic dipole nuclear

Nuclear magnetic dipole moment of ground (g) and excited (e) state (in nuclear magnetons, n.m.)... 

The magnetic hyperfine splitting, the Zeeman effect, arises from the interaction between the nuclear magnetic dipole moment and the magnetic field H at the nucleus. This interaction gives rise to six transitions the separation between the peaks in the spectrum is proportional to the magnetic field at the nucleus. 

Closed shell molecules in the rotational ground state have no net magnetic dipole moment m apart from nuclear magnetic dipole moments. However, when molecules rotate with angular momentum /, they acquire a net rotational magnetic moment... 

TABLE 5. Theoretical results for the magnetic dipole coupling constant. For the nuclear magnetic dipole, bulk distribution (present paper and [11]) and surface distribution [22]. 

In quantum mechanics this then becomes the vector product of the nuclear magnetic dipole moment and the distance vector between an electron i and the field-creating nucleus I (60)... 

Further evidence for this mechanism of spin-spin coupling in liquids is the fact that the coupling dies off as the number of chemical bonds separating the two nuclei increases. Moreover, the fact that couplings between trans protons in olefins are greater than between cis protons is incompatible with a direct interaction between the two nuclear magnetic dipoles. 

NMR transitions are between energy levels that correspond to different orientations of the nuclear magnetic dipole moment in an applied magnetic field B. The classical energy of interaction between an isolated nuclear magnetic moment fiN and B is2... 

By assuming an Arrhenius type temperature relation for both the diffusional jumps and r, we can use the asymptotic behavior of /(to) and T, as a function of temperature to determine the activation energy of motion (an example is given in the next section). We furthermore note that the interpretation of an NMR experiment in terms of diffusional motion requires the assumption of a defined microscopic model of atomic motion (migration) in order to obtain the correct relationships between the ensemble average of the molecular motion of the nuclear magnetic dipoles and both the spectral density and the spin-lattice relaxation time Tt. There are other relaxation times, such as the spin-spin relaxation time T2, which describes the... 

When energy equivalent to the difference between the energy levels is applied to the system, a transition from the lower to the higher energy level occurs. In NMR spectroscopy, the applied energy that allows this nuclear magnetic dipole transition to occur is a radio-frequency magnetic field, Hx, which is applied perpendicularly to H0. 

Mk denotes the nuclear magnetic dipole moment operator, obtained by multiplication of the nuclear spin operator IA- by the magnetogiric factor yK. 

The ground-state electronic configurations (levels) of neutral and singly ionized berkelium were identified as 5f 7s2 (6H15/2) and Sf s1 (7H8), respectively (82). A nuclear magnetic dipole moment of 1.5 nuclear magnetons (61) and a quadrupole moment of 4.7 barns (83) were determined for 249Bk, based on analysis of the hyperfine structure in the berkelium emission spectrum. 

Spectra of solids arc complicated, because of the multiplicity of parameters involved, especially by anisotropic interactions as dipolar coupling. Many techniques both experimental or computational have been developed for interpretation. A technique particularly useful for catalysis permits to selectively suppress anisotropic contributions by mechanical rotation of the sample (magic angle spinning, MASNMR) and by rotation of the nuclear magnetic dipoles with sequences of radiofrcqucncy pulses. 

This energy, when using the explicit formulas for the nuclear magnetic dipole moments, becomes... 

Nuclear magnetic dipole moment (nuclear magnetons) nuclear quadrupole moment (barns nonzero if I > 1)... 

Transformation of coordinates for the nuclear magnetic dipole and electric quadrupole terms... 

We recall from chapter 4 that there are many individual types of interaction which involve the nuclear magnetic dipole and electric quadrupole moments. Let us take just three of these to exemplify how the effective Hamiltonian is constructed. They are as follows ... 

For the case of two point nuclear magnetic dipole moments, the remaining matrix element in (11.100) is calculated for 0 = 0, enabling us to define the dipolar parameter... 

---